What you see on the desktop isn't a FAT filesystem on the SPI Flash chip.

The UF2 bootloader uses the USB Mass Storage protocol to talk to the computer, but it isn't a real filesystem. The bootloader hijacks USB commands to read or write files and puts the information where it wants.

If you want to use the Adafruit_SPIFlash library, start with the fatfs_format example to create the filesystem.

Would seem to indicate that basic SPI communication with the flash chip is not working, either because the code is not aware of the hardware details of the board on which it is being used (SPI bus, chip select, SPI mode, etc) or because something is physically wrong.

Alas the downside of that tiny package means that the flash signals can't exactly be probed (apart from the chip select, which should be on R2 pullup if you can find that). Probably worth making sure the code is using the appropriate hardware details for the board itself. Or to test the hardware, perhaps try CircuitPython at least temporarily.